Average Consensus Estimation And Optimization Of The Distributed Networks

Distributed averaging algorithms have extremely attracted interest for applicationsin networked systems because nodes maintain simple state information and exchangeinformation with only their one-hop neighbors. Therefore, it is not necessary to establishor maintain complicated routing structures. On the other hand, there are no bottlenecklinks, such as tree or ring structure, caused by that network computations may becompromised, lost, or jammed by an adversary. And over all, average consensusalgorithms have the attractive property that the eventually computed value is avaiblethroughtout the network, enabling a network user to query any node and immediatelyreceive the result, rather than querying from a fusion center and waiting for the response.Furthermore, the eventually computed value is exactly the average of the initial nodemeasurements that has received much attention due to the wide applications in wirelesssensor networks (WSNs). This dissertation focuses on average consensus estimation andoptimization for the distributed communication networks. The main contributions andoriginality contained in this dissertation are as follows:①Average consensus in sensor networks via broadcast multi-gossipMotivated by applications to wireless sensor, peer-to-peer, and ad hoc networks, adistributed algorithm called broadcast-based multi-gossiping algorithm (BMGA) isproposed, which is designed for exchanging information and computing in an arbitrarilyconnected network of nodes. Unlike the traditional randomized gossip algorithms,push-sum mechanism based BMGA preserves the sums and weights, and admitsstochastic diffusion matrices which need not be doubly stochastic. Based on the theoryof weak ergodicity and message spreading, a lower bound on the weight is derived andan approximate value for this bound is worked out. By defining a potential function,BMGA converges almost surely to the average of initial node measurements withprobability one. Specifically, the upper bounds on the diffusion speed,-convergencetime and the number of radio transmissions are provided. Finally, a numerical exampleis presented to assess and compare the communication cost of several gossip-basedalgorithms to achieve a given performance for consensus.②Accelerated average consensus in multi-agent networks via state predictionThis section considers the double-integrator consensus speeding up problem formulti-agent networks (MANs) asymptotically achieving distributed weighted average. First, basic theoretical analysis is carried out and several necessary and sufficientconditions are derived to ensure convergence to weighted average for both directed andundirected networks, but the convergence is generally slow. In order to improve the rateof convergence, an approach is proposed to accelerate consensus by utilizing a linearpredictor to predict future node state on the basis of the current and outdated node state.The local iterative algorithm then becomes a convex weighted sum of the originalconsensus update iteration and the prediction, which allows for a significant increase inthe rate of convergence towards weighted average consensus because redundant satesare bypassed. Additionally, the feasible region of mixing parameters and optimal mixingparameters are determined for undirected networks. It is worth pointing out that theaccelerated framework has tapped the maximum potential to the utmost, from both thecurrent and outdated state stored in the memory, to improve the rate of convergencewithout increasing the computational and memorial burden. Finally, a simulationexample is provided to demonstrate the effectiveness of our theoretical results.③Weighted average prediction for multi-agent networks with single integratordynamicsThis section studies how to improve the robustness and the convergence speed forachieving the desired weighted average consensus for multi-agent networks. To do this,an improved weighted average prediction is introduced and the network model thenbecomes a delayed network model with neutral-type. By the similar technique analyzingthe Hopf bifurcation, an upper bound of communication delay is derived for multi-agentnetworks to achieve average consensus. Additionally, the given results show that theimproved weighted average prediction can not only improve the robustness againstcommunication delay but also the convergence speed compared with the original system.Finally, two simulation examples are provided to demonstrate the effectiveness of ourtheoretical results.④Cooperative distributed optimization in multi-agent networks with delayedsubgradientsThis section considers a distributed cooperative optimization problem over acomputational multi-agent network with delay, where each agent has local access to itsconvex cost function, and jointly minimizes the cost function over the whole network.To solve this problem, an algorithm whcih is based on dual averaging updates anddelayed subgradient information is developed, and furthermore, we also analyze itsconvergence properties for a diminishing step-size by utilizing Bregman-distance functions. Moreover, the sharp bounds on convergence rates are provided as a functionof the network size and topology embodied in the inverse spectral gap. Finally, anumerical example is presented to assess and compare the performance benefits withseveral similar algorithms.